MF19: the Cambridge 9709 list of formulae and tables

By Fatema Bhatt, Founder, STEM-Tutor · Updated October 2026

MF19 is the list of formulae and statistical tables you get in every Cambridge AS and A Level Mathematics (9709) exam. It is shared with Further Mathematics (9231), so not everything in it is for you. Here is what 9709 students actually use, and what is missing.

What MF19 is

MF19 is Cambridge International's List of formulae and statistical tables. A clean copy is supplied in every 9709 exam, and a copy is printed for reference in the 9709 syllabus. It is a combined list for AS and A Level Mathematics (9709) and Further Mathematics (9231). The Further Mathematics parts are in separate sections labelled Further Pure Mathematics, Further Mechanics and Further Probability & Statistics, and 9709 students can ignore them.

Pure Mathematics

• Mensuration: the volume and surface area of a sphere, the volume of a cone or pyramid, the curved surface area of a cone, and the arc length and sector area of a circle, with θ in radians.
• Algebra: the quadratic formula; the nth term and sum of an arithmetic series; the nth term, sum and sum to infinity of a geometric series; and the binomial series, both for a positive whole-number power and for a rational power with |x| < 1.
• Trigonometry: tan θ = sin θ / cos θ, the three Pythagorean identities, the compound angle formulas for sin, cos and tan, the double angle formulas, and the principal values of sin⁻¹, cos⁻¹ and tan⁻¹.
• Differentiation: a table of derivatives of xⁿ, ln x, e^x, sin x, cos x, tan x, sec x, cosec x, cot x and tan⁻¹ x, the product and quotient rules, and dy/dx for parametric equations.
• Integration: a table of integrals, including 1/(x² + a²) and 1/(x² − a²), integration by parts, and the integral of f′(x)/f(x).
• Vectors: the scalar product in component form and as |a||b| cos θ.

Mechanics

For 9709 Paper 4, MF19 gives just the four equations for uniformly accelerated motion: v = u + at, s = ½(u + v)t, s = ut + ½at² and v² = u² + 2as. Newton's laws, momentum, friction, work and power are not listed, so you must know them.

Probability & Statistics

• Summary statistics: the mean and standard deviation for ungrouped and grouped data.
• Discrete random variables: E(X) and Var(X), and the probability formula, mean and variance of the binomial, geometric and Poisson distributions.
• Continuous random variables: E(X) and Var(X) as integrals (Paper 6).
• Sampling and testing: unbiased estimators of the mean and variance, the Central Limit Theorem, and the approximate distribution of a sample proportion.

The tables

9709 students use the normal distribution function table and the critical values for the normal distribution. The t-distribution, chi-squared and Wilcoxon tables in MF19 are for Further Mathematics.

What MF19 does not give you

• Laws of logarithms, and the derivative and integral of a^x.
• The equation of a circle, gradients of perpendicular lines and other coordinate geometry.
• The trapezium rule and iteration formulas for numerical methods.
• The R cos(θ ± α) and R sin(θ ± α) forms, and the small details of solving trigonometric equations in a range.
• The chain rule and implicit differentiation, which are techniques rather than listed formulas.
• Permutations and combinations counting rules, beyond the binomial coefficient.
• The continuity correction and when to approximate a binomial or Poisson distribution by a normal one.

Using MF19: a binomial series

Expand (1 + 2x)^−½ up to the term in x², and state the values of x for which it is valid.

• MF19 gives (1 + x)ⁿ = 1 + nx + n(n − 1)x²/2! + … for rational n and |x| < 1. Replace x with 2x and use n = −½.
• Second term: n × 2x = (−½)(2x) = −x.
• Third term: n(n − 1)/2! × (2x)² = (−½)(−3/2)/2 × 4x² = (3/8) × 4x² = 1.5x².
• So (1 + 2x)^−½ ≈ 1 − x + 1.5x², valid for |2x| < 1, that is |x| < ½.

Using MF19: integration with a standard form

Find the integral of 1/(x² + 9) with respect to x.

• MF19 gives the integral of 1/(x² + a²) as (1/a) tan⁻¹(x/a). Here a = 3.
• So the integral is (1/3) tan⁻¹(x/3) + c. MF19 omits the constant, so remember to add it.

Using the normal tables

X ~ N(30, 5²). Find P(X > 38).

• Standardise: z = (38 − 30) / 5 = 1.6.
• The normal distribution function table gives Φ(1.6) = 0.9452.
• P(X > 38) = 1 − 0.9452 = 0.0548.

How to train with MF19

1. Download MF19 from the Cambridge website or use the copy in the 9709 syllabus, and use it for every past paper.
2. Cross out the Further Mathematics sections on your practice copy so you do not waste time searching them.
3. Learn the list of what is not given above, with an example of each.
4. Practise reading the normal table quickly, including the symmetry rule Φ(−z) = 1 − Φ(z).

Common mistakes

• Searching the Further Mathematics sections for a formula 9709 does not use.
• Forgetting that the arc length and sector formulas need θ in radians.
• Using the binomial series for a rational power without stating where it is valid.
• Forgetting the constant of integration, which MF19 leaves out.

Practice questions

Try each one before opening the answer.

Frequently asked questions

What does MF19 stand for?

It is the code Cambridge uses for its List of formulae and statistical tables for AS and A Level Mathematics and Further Mathematics.

Is MF19 given in every 9709 paper?

Yes. Cambridge supplies MF19 in the examinations for 9709.

Can I use an older formula list?

Use MF19 with current papers. Older syllabuses used different lists, so their contents do not match today's exams.

Where can I download MF19?

Cambridge International publishes it as a free PDF: List MF19, List of formulae and statistical tables (16 pages). Practise with a printed copy so you know where everything is.

Key takeaways

• MF19 is supplied in every 9709 exam.
• It is shared with Further Maths: ignore the Further sections.
• Pure, mechanics (four suvat equations), statistics and normal tables.
• Logs, circles, the trapezium rule and R-forms are not given.
• Practise with it for every past paper.

Related guides

• Cambridge 9709 syllabus
• 9709 past papers
• Binomial expansion
• The normal distribution